A group of friends will go on a weekend camping trip and split the cost of gas
equally. The cost that each person will pay for gas is inversely proportional to the
number of people who go on the trip. If four friends go on the trip, each person pays
$23 for gas. Write an equation that describes the relationship between cost (c) that
each person pays for gas, and the number of people on the trip (n).
C = 92/n
C= n/0.17
C = 5.75n
C = 5.75/n
9514 1404 393
Answer:
(a) C = 92/n
Step-by-step explanation:
The "inversely proportional" relation is represented by the equation ...
C = k/n
The value of k can be found from the given values of C and n.
23 = k/4
23×4 = k = 92
Then the relationship is ...
C = 92/n
Air-USA has a policy of booking as many as 22 people on an airplane that can only seat 20 people. (Past studies have revealed that only 82% of the booked passengers actually show up for the flight.) a) Find the probability that if Air-USA books 22 people, not enough seats will be available. Round your answer to 4 decimal places. P ( X > 20 )
Answer:
The answer is "0.07404893".
Step-by-step explanation:
Applying the binomial distribution:
[tex]n = 22\\\\p= 82\%=0.82\\\\q = 1-0.82 = 0.18\\\\[/tex]
Calculating the probability for not enough seats:
[tex]=P(X>20)\\\\= P(21) + P(22)\\\\[/tex]
[tex]= \binom{22}{21} (0.82)^{21}(0.18)^1+ \binom{22}{22} (0.82)^{22}(0.18)[/tex]
[tex]=0 .06134598+ 0.01270295\\\\=0.07404893[/tex]
enter the number that belongs in the green box (please enter both numbers for the empty boxes)
Given:
The equation is:
[tex]5x-2=4+2x[/tex]
To find:
The number that belongs in the green box and another box.
Solution:
We have,
[tex]5x-2=4+2x[/tex]
Subtracting 2x from both sides, we get
[tex]5x-2-2x=4+2x-2x[/tex]
[tex]3x-2=4[/tex]
Adding 2 on both sides, we get
[tex]3x-2+2=4+2[/tex]
[tex]3x=6[/tex]
We need to divide both sides by 3 to isolate the variable x.
On dividing both side by 3, we get
[tex]\dfrac{3x}{3}=\dfrac{6}{3}[/tex]
Therefore, the missing values are 3 and 3, and the required equation is [tex]\dfrac{3x}{3}=\dfrac{6}{3}[/tex].
Clue is a board game in which you must deduce three details surrounding a murder. In the original game of Clue, the guilty person can be chosen from 66 people, and there are 66 different possible weapons and 99 possible rooms. At one point in the game, you have narrowed the possibilities down to 44 people, 55 weapons, and 77 rooms. What is the probability of making a random guess of the guilty person, murder weapon, and location from your narrowed-down choices, and the guess being correct
Answer:
The probability of making a correct random guess is 0.00053%.
Step-by-step explanation:
Since Clue is a board game in which you must deduce three details surrounding a murder, and in the original game of Clue, the guilty person can be chosen from 66 people, and there are 66 different possible weapons and 99 possible rooms, and at one point in the game, you have narrowed the possibilities down to 44 people, 55 weapons, and 77 rooms, to determine what is the probability of making a random guess of the guilty person, murder weapon, and location from your narrowed-down choices , and the guess being correct, the following calculation must be performed:
(1 / (44x55x77)) x 100 = X
(1 / 186,340) x 100 = X
0.0005366 = X
Therefore, the probability of making a correct random guess is 0.00053%.
A plane flying horizontally at an altitude of 3 mi and a speed of 460 mi/h passes directly over a radar station. Find the rate at which the distance from the plane to the station is increasing when it is 4 mi away from the station (Round your answer to the nearest whole number.) 368 X mi/h Enhanced Feedback Please try again. Keep in mind that distance - (altitude)2 + (horizontal distance)? (or y = x + n ). Differentiate with respect to con both sides of the equation, using the Chain Rule, to solve for the given speed of the plane is x.
Answer:
[tex]\frac{dy}{dt}=304mi/h[/tex]
Step-by-step explanation:
From the question we are told that:
Height of Plane [tex]h=3mi[/tex]
Speed [tex]\frac{dx}{dt}=460mi/h[/tex]
Distance from station [tex]d=4mi[/tex]
Generally the equation for The Pythagoras Theorem is is mathematically given by
[tex]x^2+3^2=y^2[/tex]
For y=d
[tex]x^2+3^2=d^2[/tex]
[tex]x^2+3^2=4^2[/tex]
[tex]x=\sqrt{7}[/tex]
Therefore
[tex]x^2+3^2=y^2[/tex]
Differentiating with respect to time t we have
[tex]2x\frac{dx}{dt}=2y\frac{dy}{dt}[/tex]
[tex]\frac{dy}{dt}=\frac{x}{y}\frac{dx}{dt}[/tex]
[tex]\frac{dy}{dt}=\frac{\sqrt{7}}{4} *460[/tex]
[tex]\frac{dy}{dt}=304.2614008mi/h[/tex]
[tex]\frac{dy}{dt}=304mi/h[/tex]
PLEASE HELPPPPPPPPP!!!!!!!!!!!
Calculate the minimum number of subjects needed for a research study regarding the proportion of respondents who reported a history of diabetes using the following criteria:
95% confidence, within 5 percentage points, and a previous estimate is not known.
Answer:
The minimum number of subjects needed is 385.
Step-by-step explanation:
In a sample with a number n of people surveyed with a probability of a success of [tex]\pi[/tex], and a confidence level of [tex]1-\alpha[/tex], we have the following confidence interval of proportions.
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
The margin of error is:
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
95% confidence, within 5 percentage points, and a previous estimate is not known.
The sample size is n for which M = 0.05. We don't know the true proportion, so we use [tex]\pi = 0.5[/tex]
Then
[tex]M = z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
[tex]0.05 = 1.96\sqrt{\frac{0.5*0.5}{n}}[/tex]
[tex]0.05\sqrt{n} = 1.96*0.5[/tex]
[tex]\sqrt{n} = \frac{1.96*0.5}{0.05}[/tex]
[tex](\sqrt{n})^2 = (\frac{1.96*0.5}{0.05})^2[/tex]
[tex]n = 384.16[/tex]
Rounding up:
The minimum number of subjects needed is 385.
Write the expression as a trinomial (3a+4)(8-a).
Answer:
-3a² + 20a + 32
Step-by-step explanation:
(3a+4)(8-a)
24a - 3a² + 32 - 4a
-3a² + 24a - 4a + 32
-3a² + 20a + 32
solve above question
Find the length of the leg x
Answer:
12.65
Step-by-step explanation:
Pythagoras :
c² = a² + b²
c is the Hypotenuse (the side opposite of the 90 degree angle).
a and b are the side legs.
so, here we have
14² = 6² + b²
196 = 36 + b²
160 = b²
b = sqrt(160) = sqrt(16×10) = 4×sqrt(10) = 12.65
16 is what percent of 4
Answer:
400%
Step-by-step explanation:
Is means equals and of means multiply
16 = P *4
Divide each side by 4
16/4 = P4/4
4 = P
Change to a percent by multiply by 100 and adding the percent sign
400% = P
Infues Gentamicin 100 mg in 100ml in 15 minutes. What will you set the infusion pump at ml/hr
9514 1404 393
Answer:
400 mL/h
Step-by-step explanation:
The required rate is ...
(100 mL)/(1/4 h) = 100×(4/1) mL/h = 400 mL/h
Which piecewise function represents the graph?
the function that connects the point (0;1) with the point (-1;0) is the graph
There are 6 people named A,B,C,D,E,F. The people named A,B, and C are all over the age of 40. The people named D,E,F are all under the age of 40. How many different orders are there for the people to sit on a bench, if both ends of the bench must be occupied by someone over the age of 40?
About 3% of the population has a particular genetic mutation. 200 people are randomly selected.
Find the mean for the number of people with the genetic mutation in such groups of 200
Answer:
6
Step-by-step explanation:
200. Move decimal twice to the left. 1% of 200 is 2. 2*3 is 6.
Solve the following system of equations using the elimination method.
5x - 5y = 10
6x - 4y= 4
A) (-3,5)
B) (2-7)
C) (-1,-5)
D) (-2,-4)
Answer:
D. (-2,-4)
Step-by-step explanation:
When given multi-choice questions like these and you're time bound, substitute the provided answers into the question and see if you'll get the figure beside the '='.
So, using D answers as example 1.
let -2 be x and -4 be y
Substitute these answers into the question.
5(-2)-5(-4)=10
-10+20=10 (+20 because when 2 negative values multiply each other, the operator becomes positive and so is the answer)
10=10
This means the answers provided for D(-2,-4) is the right answer.
PS: Please use or adopt this strategy to solve such questions ONLY when you've been provided with multiple answers to choose from. Plus, it also helps save time.
Thanks
Find the value of x round to the nearest tenth.
9514 1404 393
Answer:
117.9°
Step-by-step explanation:
Solving the Law of Cosines equation for C, we get ...
C = arccos((a² +b² -c²)/(2ab))
Filling in the values from the figure, we find the angle X to be ...
X = arccos((y² +z² -x²)/(2yz)) = arccos((55² +50² -90²)/(2·55·50))
X = arccos(-2575/5500) ≈ 117.9°
Hey I need helping with solving thank you
Answer:
the answer to this equation is c (10)
Let U be the event that a randomly chosen employee of an insurance company has been an underwriter. Let C be the event that a randomly chosen employee of an insurance company has been a claims adjuster. Identify the answer which expresses the following with correct notation: Of all the employees of an insurance company who have been underwriters, the probability that a randomly chosen employee of an insurance company has been a claims adjuster. Select the correct answer below:
a. P(C) AND P(U)
b. P(C|U)
c. P(U|C)
d. P(U AND C)
Answer:
b. P(C|U)
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
In this question:
Event U: Event that a randomly chosen employee of an insurance company has been an underwriter.
Event C: Event that a randomly chosen employee of an insurance company has been a claims adjuster.
Select the correct answer below:
Claims adjuster given that it has been an underwriter, so P(C|U), and the correct answer is given by option b.
Triangles ABC and DEF are similar triangles. What are the lengths of the unknown sides?
A)
DF = 39 cm; DE = 15 cm
B)
DF = 48 cm; DE = 52 cm
C)
DF = 65 cm; DE = 25 cm
D)
DF = 52 cm; DE = 48 cm
Answer:
D)
DF = 52
AB = 48
Step-by-step explanation:
Use the two lengths of sides already given.
Divide to find the scale factor:
20 / 5 = 4
Scale factor: 4
Now multiply to find the unknown sides:
13 × 4 = 52
12 × 4 = 48
DF = 52
AB = 48
Hope this helped.
Please help me to find this answer
Step-by-step explanation:
question 1
angle DBA=90°, meaning to find m<D you have to add 90+38 then subtract by 180, because ABD is a triangle
90+18+m<D=180
108+m<D=180
m<D=180-108
=72°
question 2
m<D again in this case angle ABD is also 90
m<D=180-(90+48)
=180-138
=42°
I hope this helps
Please solve this l am in many problem please please please please help me
Answer:
h) a+20 = 80 (vert. opp angles)
a = 60
i) 3a+48 = 180
3a = 132
a = 44
a) 3x + 2x = 180
5x = 180
x = 36
∡y = 72
∡z = 108
∡r = 144
∡x = 180-144 = 36
b) p:b = 3:1
4u = 180
u = 45
∡p = 135
∡b = 45
∡q = ∡p = 135 (vert. opp)
∡a = ∡b = 45 (vert. opp)
Answer:
hello,
as i have taken the time to draw the picture
Step-by-step explanation:
Which expression is equivalent to
-32 3/5
-8
-3/325
3/325
1/8
Answer:
[tex]-32^\frac{3}{5} = -8[/tex]
Step-by-step explanation:
Given
[tex]-32^\frac{3}{5}[/tex]
Required
The equivalent expression
We have:
[tex]-32^\frac{3}{5}[/tex]
Rewrite as:
[tex]-32^\frac{3}{5} = (-32)^\frac{3}{5}[/tex]
Expand
[tex]-32^\frac{3}{5} = (-2^5)^\frac{3}{5}[/tex]
Remove bracket
[tex]-32^\frac{3}{5} = -2^\frac{5*3}{5}[/tex]
[tex]-32^\frac{3}{5} = -2^3[/tex]
[tex]-32^\frac{3}{5} = -8[/tex]
Please answer! These r my last questions
Answer:
8. -2a+14
9. w=3/2
Step-by-step explanation:
8.
The distributive property states that we can multiply each component in the parenthesis separately by the number on the outside, and then add that up to get our final answer.
For -2(a-7), this means that we can multiply -2 by a and then -2 by -7 (as 2 is the number on the outside, and a and -7 are the components in the parenthesis), add them up, and get our answer. This can be expressed as
-2 * a + (-2) * (-7) = final answer
= -2 * a + 14
We know that -2 * -7 = 14 because 2 * 7 = 14, and the two negatives in multiplication cancel each other out
9.
Using the subtraction property of equality, we can isolate the variable (w) and its coefficient (-2/3) by subtracting 5, resulting in
(-2/3)w = 4-5 = -1
Next, we can use the multiplication property of equality to isolate the w. To isolate the w, we can multiply its coefficient by its reciprocal. The reciprocal is the fraction flipped over. For (-2/3), its reciprocal is (-3/2), flipping the 2 and 3. We can multiply both sides by (-3/2) to get
w = (-3/2)
To check this, we can plug (-3/2) for w in our original equation, so
(-2/3) * (-3/2) + 5 = 4
-1 + 5 = 4
4 = 4
This works!
How many permutations of letter of the word APPLE are there?
Answer:
There are 60 permutations.
Step-by-step explanation:
Arrangements formula:
The number of possible arrangements of n elements is given by:
[tex]A_n = n![/tex]
With repetition:
For each element that repeats, with [tex]n_1, n_2, ..., n_n[/tex] times, the formula is:
[tex]A_n^{n_1,n_2,...,n_n} = \frac{n!}{n_1!n_2!...n_n}[/tex]
In this question:
Apple has 5 letters.
P appears two times. So
[tex]A _5^{2} = \frac{5!}{2!} = 60[/tex]
There are 60 permutations.
help please i’ll give brainliest
Answer:
3rd option
..................[tex]A) \frac{4-2}{2-1} =2[/tex]
[tex]B)\frac{1-0.5}{4-2} =0.25[/tex]
[tex]C)>2[/tex]
[tex]D) 1[/tex]
~OAmalOHopeO
Answer:
The third one is your answer
A chef is going to use a mixture two different brands of Italian dressing the first spring and days 5% vinegar the second brain contains 15% vinegar the sheriff wants to make 390$ ml addressing that is 9% vinegar how much of each brand should she use
I guess the chef is making the mixture for the sheriff... Let x be the amount of dressing with 5% vinegar that is required, and y the amount of 15% vinegar dressing (both amounts in mL).
The sheriff wants 390 mL of the mixed dressing, so that
x + y = 390
x mL of the 5% dressing contains 0.05x mL of vinegar, while y mL of the 15% dressing contains 0.15y mL of vinegar. The resulting mixture should have a concentration of 9% vinegar, so that it contains 0.09 (390 mL) = 35.1 mL of vinegar. This means
0.05x + 0.15y = 35.1
Solve for x and y :
y = 390 - x
0.05x + 0.15 (390 - x) = 35.1
0.05x + 58.5 - 0.15x = 35.1
23.4 = 0.10x
x = 234
y = 156
According to Statcast, the average left field home run travels 378 feet and reaches a maximum height of 81 feet. Assuming the ball is hit from 3 feet in the air, write an equation for its height as it travels from home plate.
Answer:
H = V0y t - 1/2 g t^2 equation for vertical height of object with initial speed (V0y = V0 sin theta)
If H is to be considered an absolute value from t = 0
h = H + 3 = V0y t - 1/2 g t^2 + 3 where h is height from ground
> There are 14 books on a shelf. 6 of these books are new. The rest of them are used (a) What is the ratio of new books to used books? (b) What is the ratio of used books to all books on the shelf
Answer:
a) 6:8
Because you have 14 books total if you substract 14 - 6= 8, so now you have
14 Books total
6 New Books
8 Used Books.
So, the ratio of new books to used books is 6:8 or if you simplified is 3:4.
b) 8:14
Because you have 8 used books compare to 14 books total. If you simplified your fraction you'll have 4:7
Step-by-step explanation:
Put the following equation of a line into slope-intercept form, simplifying all
fractions.
18x + 3y = -18
Answer:
y = -6x -6
Step-by-step explanation:
The general form of the equation of a line in the slope-intercept form may be given as
y = mx + c where
m is the slope and c is the intercept
Hence given the equation
18x + 3y = -18
subtract 18x from both sides
3y = -18x - 18
Divide both sides of the equation by 3
y = -6x -6
This is the equation in the slope - intercept form with -6 as the slope and -6 as the intercept
